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znimon Group Title

Solve the non-linear inequality. Express the solution in interval notation. x^4 is greater than x^2

  • one year ago
  • one year ago

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  1. znimon Group Title
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    \[x^4>x^2\]

    • one year ago
  2. znimon Group Title
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    I take the square root of both sides and get the plus or minus square root of x^2 is greater than x, then I take the square root of x^2 and x to get x is greater than the plus or minus square root of x

    • one year ago
  3. sriramkumar Group Title
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    \[x ^{4}>x ^{2}\] \[x ^{4}-x ^{2}>0\] \[x ^{2}(x ^{2}-1)>0\] \[x ^{2}>0 or x ^{2}>1\] x>0 or x<-1 or x>1 then x<-1 and x>0 will be the interval...

    • one year ago
  4. klimenkov Group Title
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    \(x^2(x^2-1)>0\) divide it by \(x^2\): \((x-1)(x+1)>0\) \(x\in(-\infty;-1)\bigcup(1;\infty)\)

    • one year ago
  5. znimon Group Title
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    why is it greater than 0

    • one year ago
  6. znimon Group Title
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    oh subtract the x^2?

    • one year ago
  7. sriramkumar Group Title
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    yep//....

    • one year ago
  8. sriramkumar Group Title
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    @znimon understood the process?

    • one year ago
  9. znimon Group Title
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    almost, what about after x^2(x^2-1) is greater than 0

    • one year ago
  10. klimenkov Group Title
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    \(x^2\) is always bigger than 0. It equals 0 when \(x=0\). But it doesn't satisfy the inequality.

    • one year ago
  11. sriramkumar Group Title
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    took x^2 common in both the terms....

    • one year ago
  12. znimon Group Title
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    yep got that

    • one year ago
  13. sriramkumar Group Title
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    nops.. while splitting the inequality x has to be >0

    • one year ago
  14. znimon Group Title
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    will you break it down after the x^2(x^2-1) is greater than 0

    • one year ago
  15. sriramkumar Group Title
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    yep.... both the split terms are compared to the inequalities...

    • one year ago
  16. znimon Group Title
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    I understand how it works so I need to find all the solutions for x that satisfy the inequality

    • one year ago
  17. znimon Group Title
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    thanks now I'll try some on my own. Will you recommend a problem that has the same properties?

    • one year ago
  18. znimon Group Title
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    @sriramkumar

    • one year ago
  19. sriramkumar Group Title
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    try this one... \[x ^{8}-x ^{2}<0\] remeber x^3 has different properties when compared with x^2 .... have a good time!!!!1

    • one year ago
  20. znimon Group Title
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    thanks

    • one year ago
  21. sriramkumar Group Title
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    @znimon you're welcome :)))))))))))))))))

    • one year ago
  22. oldrin.bataku Group Title
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    \[\ \ x^4\ge x^2\\ \ \ x^2[x^2]\ge x^2\\x^2\text{ is either 0 non-zero.}\\ \text{if }x^2\text{ is 0,}\\ \ \ 0\times0=0\\ \ \ 0 = 0\\ \text{therefore }x^2[x^2]\ge x^2\\ \text{otherwise,}\\ \ \ x^2\ge1\\ \ \ |x|\ge\sqrt1\]

    • one year ago
  23. oldrin.bataku Group Title
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    is either 0 or non-zero **

    • one year ago
  24. znimon Group Title
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    solution is \[x <0, x <1] so (negative infinity, to 0 not including zero)?

    • one year ago
  25. znimon Group Title
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    for x^3-x^2 is less than 0

    • one year ago
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